In a disk storage apparatus, the position of a read/write head, the number of revolutions of a spindle motor which rotates a disk, and the like are controlled by means of a digital closed-loop by an internal digital microcomputer. As an example, the position control of the read/write head is described in the following. A well-known positioning mechanism of a magnetic disk apparatus is such that a voice coil motor is used as the driving source of a head. A conventional example of controlling the voice coil motor by means of a pulse is disclosed in Japanese PUPA 64-89088. In the conventional example, a manipulated pulse modulated by means of pulse width modulation (PWM) is used to operate the voice coil motor. However, since there is a limit in a variable pulse width under PWM control, it is difficult to perform adaptive control for maintaining optimum performance at all times, regardless of such variable parameters in a disk storage apparatus as output characteristics of a voice coil motor, inertial torque of a head arm, and force given to the head arm by a flexible cable attached to the head arm. Further, there is also a limit in the reduction of power consumption. In the following, the reason why the adaptive control is conventionally impossible is described in detail.
Consider the equation of motion of a read/write head in discrete time. That is, if it is assumed that the position of a head at a time n+1 is y.sub.n+1 then EQU y.sub.n+1 =a.sub.1 y.sub.n +a.sub.2 y.sub.n-1 +b.sub.1 u.sub.n +b.sub.2 u.sub.n-1 ( 1)
where u.sub.n is a current which flows through a voice coil, and a.sub.1, a.sub.2, b.sub.1, b.sub.2, and b.sub.3 are coefficients which depend on variable parameters.
In expression (1), if ##EQU1## Then, y.sub.n+1 at a time n+1 will vanish. Now consider whether there is stable input which causes y.sub.n+1 to vanish
Expression (1) can be written by z transformation as follows (see "Digital Control" Katsuhisa Furuta, Coronasha, 1989, p.32): EQU zY=a.sub.1 Y+a.sub.2 z.sup.-1 Y+b.sub.1 u+b.sub.2 z.sup.-1 u+b.sub.3 z.sup.-2 u
It follows that: ##EQU2## Now, Y=0 is assumed. That is, the value (zero) of z is determined so that the numerator becomes zero. If Y=0, the following expression can be obtained from expression (2): EQU b.sub.1 z.sup.2 +b.sub.2 z+b.sub.3 =0 (3)
However, z which satisfies expression (3), that is, zero, is not necessarily within a unit circle in complex space, and therefore it is impossible to perform adaptive control for maintaining optimum control at all times, regardless of variable parameters (see opus citatum, p.218).